The present invention generally relates to loudspeakers that utilize aligned acoustic power sources (“line arrays”) and to the problem of undesirable grating lobes produced by line arrays. The invention particularly involves a horn structure, and a method for which can be used with multiple aligned drivers to control normally occurring grating lobes produced by the driver alignment.
Line arrays are well known for their directional characteristics and ability to project acoustic power from multiple acoustic power sources over large distances. However, the disadvantage of line arrays is that grating lobes develop when the distance between the acoustic sources of the array is one wavelength or larger. To achieve a highest possible operating frequency and high output power without grating lobes, one needs to use a large number of very small sources. Increasing the number of elements increases the number of parts and connections, which makes manufacturing difficult. It is also difficult to obtain the necessary power out of very small transducers.
Currently, there are many variations on the line array. Most variations focus on changing the signal that goes to each element. Line arrays have been made where the signal magnitude, signal phase, and signal frequency content are altered for each element in the array. More often than not this decreases the maximum on axis power of the array. Also, though gain and phase shading can alter the width of the main lobe and structure of the side lobes, it is not possible to mitigate grating lobes.
The invention can be understood from a mathematical model of the line array. The acoustic pressure in the far field of a line array of N sources, each of which has directionality Hs(θ), is:
      P    ⁡          (              r        ,        θ        ,        t            )        =            ∑              i        =        1            N        ⁢                  ⁢                            H          s                ⁡                  (          θ          )                    ⁢              1                  r          i                    ⁢              ⅇ                  j          ⁡                      (                                          ω                ⁢                                                                  ⁢                t                            -                              kr                i                                      )                              where θ is the angle, ri is the distance from the ith source to the point in space [r, θ], t is time, ω is the frequency in radians per second, and k is the wave number where ω=kc and c is the wave propagation speed. The directionality of an omni directional source is 1 everywhere (H0(θ)=1) so one can multiply any term in the equation above by the directionality of an omni and the acoustic pressure remains the same. Also the directionality of an individual source can be factored out of the sum:
      P    ⁡          (              r        ,        θ        ,        t            )        =                    H        s            ⁡              (        θ        )              ⁢          (                        ∑                      i            =            1                    N                ⁢                                  ⁢                                            H              o                        ⁡                          (              θ              )                                ⁢                      1                          r              i                                ⁢                      ⅇ                          j              ⁡                              (                                                      ω                    ⁢                                                                                  ⁢                    t                                    -                                      kr                    i                                                  )                                                        )      In this form it can be seen that the directionality of an array of aligned sources is equal to the directionality of an array of omni directional sources multiplied by the directionality of an individual source. This is called the product theorem.
For an array of omni directional sources in a straight line, each separated by distance d the directionality is:
            P      ao        ⁡          (              r        ,        θ        ,        t            )        =            1      r        ⁢                  ⅇ                  j          ⁡                      (                                          ω                ⁢                                                                  ⁢                t                            -              kr                        )                              ⁡              (                              sin            ⁡                          (                                                N                  2                                ⁢                kd                ⁢                                                                  ⁢                                  sin                  ⁡                                      (                    θ                    )                                                              )                                            sin            ⁡                          (                                                1                  2                                ⁢                kd                ⁢                                                                  ⁢                                  sin                  ⁡                                      (                    θ                    )                                                              )                                      )            There are maxima in the absolute value of this function when:
                sin      ⁡              (        θ        )                  =            m      ⁢                          ⁢      λ        d  where m is any integer. The term |sin(θ)| has a maximum of 1, so there will be more than one maxima when d>λ. These are called grating lobes.
The present invention provides a horn structure for a line array of acoustic power sources that controls these undesirable grating lobes, as well as a method of designing such a horn. Referring to the product theorem for the directionality of an array of aligned sources, the invention uses horn loading to effectively choose a directionality for an individual source which is zero (or very small) in those directions where one expects grating lobes. Because horns achieve directionality by reflecting sound into a concentrated angle, the effect of this approach is to reflect sound that would otherwise contribute to the grating lobes, into the source's main lobe. The invention increases the highest operating frequency beyond that which the line array would normally be restricted due to the separation between acoustic power sources. It also increases the available on-axis power, and reduces the number of required acoustic power sources needed to obtain a desired power output by increasing the allowable size of each source. It is noted that the approach of the invention may be applied to any transducers of waves in linear media, including microphones, and transmitters and receivers of electromagnetic waves.